A359701 a(n) = Sum_{d|n} d^(d + n/d - 2).

1, 3, 10, 69, 626, 7812, 117650, 2097425, 43046803, 1000003158, 25937424602, 743008418676, 23298085122482, 793714774077816, 29192926025406980, 1152921504623628545, 48661191875666868482, 2185911559739084235093, 104127350297911241532842

Offset

1,2

Links

Table of n, a(n) for n=1..19.

Formula

G.f.: Sum_{k>0} k^(k-1) * x^k / (1 - k * x^k).

If p is prime, a(p) = 1 + p^(p-1).

Mathematica

a[n_] := DivisorSum[n, #^(# + n/# - 2) &]; Array[a, 20] (* Amiram Eldar, Aug 14 2023 *)

Prog

(PARI) a(n) = sumdiv(n, d, d^(d+n/d-2));
(PARI) my(N=20, x='x+O('x^N)); Vec(sum(k=1, N, k^(k-1)*x^k/(1-k*x^k)))

Crossrefs

Cf. A082245, A124923, A262843, A294956.

Sequence in context: A072638 A262843 A080526 * A308814 A342629 A232213

Adjacent sequences: A359698 A359699 A359700 * A359702 A359703 A359704

Keyword

nonn

Author

Seiichi Manyama, Jan 11 2023

Status

approved